

A083662


a(n) = a(floor(n/2)) + a(floor(n/4)), n > 0; a(0)=1.


9



1, 2, 3, 3, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34
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OFFSET

0,2


COMMENTS

A000045(n+2) = a(A131577(n))and A000045(m+2) < a(m) for m < A131577(n).  Reinhard Zumkeller, Sep 26 2009


LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000


FORMULA

For n > 0, a(n) = F([log(n)/log(2)]+3) where F(k) denotes the kth Fibonacci number. For n >= 3, F(n) appears 2^(n3) times. More generally, if p is an integer > 1 and a(n) = a(floor(n/p)) + a(floor(n/p^2)), n > 0, a(0)=1, then for n > 0, a(n) = F(floor(log(n)/log(p)) + 3).


PROG

(PARI) a(n)=if(n<1, n==0, a(n\2)+a(n\4))


CROSSREFS

Cf. A088468.
A007731, A165704, A165706.  Reinhard Zumkeller, Sep 26 2009
Sequence in context: A154404 A225577 A265531 * A256405 A130149 A053046
Adjacent sequences: A083659 A083660 A083661 * A083663 A083664 A083665


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Oct 05 2003


STATUS

approved



